Q. 114.2( 15 Votes )

# Each side o

Answer :

Let ABCD be rhombus.

We know that rhombus is type of parallelogram whose all sides are equal.

∴ *AB = BC = CD = DA =* 10 cm

Let the diagonals AC and BD intersect each other at O, where AC = 16 cm and let BD = x

We know that the diagonals of a rhombus are perpendicular bisectors of each other.

∴ ∆*AOB* is a right angle triangle, in which *OB = BD* ÷ 2 = *x* ÷ 2 and *OA = AC* ÷2 = 16 ÷ 2 = 8 cm.

Now, *AB= OA ^{2} + OB^{2}…by p*ythagoras theorem

∴ 10

^{2}= ( )

^{2}+ 8

^{2}

ie. 100 − 64 =

36 ×4 = x^{2}

∴ *x*^{2} =144

∴ *x* = 12 cm

Hence, the length of the other diagonal is 12 cm

We know that area of rhombus is,

Area of rhombus = × ( Diagonal1) × ( Diagonal2)

Hence,

Area of ABCD = × AC × BD

= × 16 × 12

= 96 cm^{2}

Hence, the area of rhombus is 96 cm^{2}

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